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Question

In square ABCD, P and Q are the midpoints of sides AB and CD respectively. If AB = 8 cm and PQ and BD intersect at O, then find the area of OPB.

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Solution

In square ABCD, P and Q are the midpoints of sides AB and CD respectively.
PQ and BD are joined which intersect each other at O.
Side of square AB = 8 cm

Area of the square ABCD=(Side)2=82=64 cm2
Diagonal BD bisects the square into two triangles equal in area
Area ABD=12×Area of square ABCD
=12×64=32cm2
P is mid point of AB of ABD,
and PQ || AD
O is the mid point of BD
OP=12AD=12×8=4cmArea ofOPB=12PB×OP=12×4×4=8cm2


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